Integral of sin(n*pi*x/L)cos(m*pi*x/L): Is n=m a Requirement?

[chota]

if i have to find the integral of

sin(n*pi*x/L) * cos(m*pi*x/L) between 0<=x<=L

is it true that this integral will be 0 every where except where n=m?

please and thank you.

 

[ravioli]

Is there a trig identity that will simplify this for us a little bit?

Spoiler

sin(u)cos(v)=\frac{1}{2}\left[sin(u+v)+sin(u-v)\right]

With this trig identity, do you suppose that the integral will be equal to zero when n is not equal to m? When n is equal to m?